In general, rotary wing aircraft of heavy or medium tonnage possess wheeled undercarriages.
It is not unusual for lighter aircraft to have undercarriages of the friction skid type.
A skid undercarriage is in principle mechanically less complex than a wheeled undercarriage, lighter in weight, and often constitutes a solution that is advantageous for landing on a variety of surfaces.
Skid undercarriages have been commonplace for many years, and were already mounted on rotorcraft such as those of B. N. Yuriev in 1910 or of Louis Brennan in 1924, or indeed in 1947 in the SNIAS SE3110M helicopter.
To summarize, a skid undercarriage comprises at least two transverse elements secured to a force take-up structure of the aircraft, and having mounted thereon a pair of longitudinally extending friction skids, for example. These skids may optionally be united at the front by a junction section referred to as a “mustache”.
Like wheeled undercarriages, and under certain conditions, skid undercarriages (and consequently rotary wing aircraft) are subjected to a phenomenon of dynamic instability known as ground resonance, with this applying in particular on helicopters for which the main rotor that provides thrust and lift is a “hinged” rotor.
This ground resonance phenomenon can occur while the rotor(s) is being brought up to speed, and above all during landing at the moment of making contact with the ground.
In the event of ground resonance, the rotor(s), the engine(s), and the gearbox(es) are subjected to vibrations that propagate through the aircraft, in particular within its force take-up structure.
It is known that each element of the aircraft, including its undercarriage, presents its own resonant frequency of vibration that depends in particular on its mass, and on its flexibility or stiffness, which are themselves a function of the shape, the dimensions, and the component materials of the element.
As a result, complex vibration can be added to or subtracted from the vibration of the aircraft as a whole so that the level of vibration increases or decreases accordingly.
In flight, the aircraft is isolated, and for any given flying speed, the level of vibration always stabilizes.
In contrast, when the aircraft is on the ground with its (main) propulsion and lift rotor(s) revolving, the vibration finds a reaction point on the landing surface that acts through the undercarriage.
Under such circumstances, the resonant frequency of the undercarriage can be in tune with the frequency of the main vibrations coming from the main propulsion and lift rotor.
In the event of the frequency of the rotor being in tune with the resonant frequency of the undercarriage, the vibration acting on the undercarriage receives additional impulses in reaction on each revolution of the blades of the main rotor.
Under such conditions, the amplitude of vibration increases quickly. Such diverging vibration and the resulting oscillation can lead to the aircraft tipping over suddenly, which can destroy it.
The risk of ground resonance appearing is greater while setting the propulsion and lift rotor(s) into motion, since frequency then rises relatively slowly. In contrast, on landing, frequency variation takes place much more quickly, so the risk of ground resonance is smaller.
More precisely, it is considered that such tilting is most likely to occur when the following frequencies are matched:                the frequency of a first mode in rolling of the aircraft, written “ωx”; and        the value written “Ω” representative of the speed of rotation of the main rotor at a given instant.        
These considerations concerning ground resonance lead to various types of undercarriage being classified as to whether they present “subcritical” or “supercritical” behavior.
Thus, in a subcritical skid undercarriage for a rotary wing aircraft, it is desired that below a nominal speed of rotation for the main rotor of the aircraft, having a value written Ωn;                the value (in radians per second, written rad/s) of the frequency of the first mode in rolling ωx of the aircraft is greater than:        the difference between firstly, the value Ω (in rad/s) of the speed of rotation of the main rotor; and        secondly, the value written “ωδ” (in rad/s) of the frequency of a first mode in lag of the blades (i.e. the frequency of lag oscillations of the blades).        
For the main rotor of a rotorcraft, the frequency ωδ of its first lag mode is of the order of half the value written “Ωn” representing the nominal speed of rotation of the rotor (where the approximation is written “±”).
In this context, the following equation can be written:ωx>Ω−ωδ=±0.5Ωn 
In addition, in a rotary wing aircraft, in the event of an engine failure, it is appropriate to consider that the aircraft is put into an autorotation mode in order to limit the consequences of a hard landing, with the speed of rotation of the rotor in autorotation being written “Ωa”, with this speed being greater than the nominal speed of rotation Ωn of the main rotor by a factor “k”.
As a result, in autorotation, the absolute value of Ωa−ωδ comes very close to the frequency of the first mode in rolling ωx so that the risk of ground resonance increases in the event of a hard landing in autorotation.
The same applies when the in-flight weight of a rotary wing aircraft is increased, in particular by adding heavy equipment on the aircraft such as weapons, or when there is a decrease in the second moment of area or the stiffness of the aircraft—including that of its undercarriage.
Under all acceptable flying configurations, it is necessary to maintain a sufficient safety margin.
Maintaining this safety margin for subcritical skid undercarriages, i.e. the margin between the absolute value |Ω−ωδ| and the value of the frequency of the first mode in rolling ωx, generally requires damping to be added between the transverse elements of the landing gear and the force take-up structure.
Thus, subcritical skid undercarriages with damping have been proposed and are said to be “rigid” or “stiff”.
By way of example, this applies to the skid undercarriage fitted to the AS350 Ecureuil helicopter.
On that aircraft, the single front transverse element is mounted internally via clamps on beams of a bottom section of the force take-up structure, while two dampers provide a transverse outside connection between said front transverse element and a partition of said structure.
At the rear, another single transverse element is mounted via clamps to a transversely central portion of the force take-up structure. It should be observed that such a skid undercarriage of the subcritical and rigid type is typically associated with flexible blades at the rear ends of the skids, as described in document FR 2 372 081 mentioned below.
Furthermore, for a skid undercarriage that is not subcritical but is instead supercritical, it is desirable for the value of the frequency of the first mode in rolling ωx to remain less than the absolute value of the difference between Ω and ωδ, which can be written:ωx<|Ω−ωδ|
In other words, with supercritical skid undercarriages, it is desirable for the frequency values Ω associated with the speed of rotation of the main rotor and ωδ of the first lag mode to pass through the value ωx of the frequency of the first roll mode (which in this case is about 0.6 times the nominal rotor frequency Ωn).
This frequency is passed through quickly because of the high accelerations and decelerations in the speed of rotation of the main rotor, respectively during takeoff and landing of the aircraft.
As a result, and under such circumstances, the normal rates of damping do not require to be as great as they do with a skid undercarriage that is subcritical and rigid.
With a supercritical skid undercarriage there is a stiffness factor “K” such that the value ωx of the frequency of the first mode in rolling is equal to the square-root of the ratio between the value of said stiffness factor K and the weight M of the aircraft.
In theory, it is therefore possible to obtain a supercritical skid undercarriage without dampers that is acceptable from the ground resonance point of view, providing it presents suitable flexibility.
For example, such an approach of the supercritical type is applied to the skid undercarriage of the AS342 Gazelle helicopter which is flexible and passes through a resonance mode.
In the AS342 Gazelle aircraft, the front transverse element is rigidly mounted to the force take-up structure via two clamps that are spaced apart transversely.
However, transversely outside those clamps, the front transverse element includes a universal joint between each skid front portion and the rigid mount location.
The universal joint provides a degree of flexibility to the ends where the skids are secured to the transverse element, and thus allow the fronts of the skids to move elastically.
At the rear, transversely on either side of a top fitting of the force take-up structure where a side brace is hinged, the rear transverse element is connected via two junction clamps to said structure.
This reduces the resonant frequency of the skids, which frequency is kept below the nominal rotation frequency of the main rotor.
Various prior art examples of skid undercarriages are mentioned below.
Document FR 1 578 594 describes a landing gear for a helicopter with skids that serve to damp the impact of landing.
To ensure that all the twisting forces are absorbed by the skids, that landing gear possesses two front elements forming offset cross-members and at least one rear transverse element, the skid being connected to said elements.
The transverse elements are pivotally mounted to the force take-up structure of the helicopter, and dampers are associated with the rear transverse element to attenuate bouncing and ground resonance of the aircraft.
Drag struts going from the structure of the helicopter to the rear transverse element are added to the landing gear, e.g. by being integrated with the rear transverse element, in order to increase the rigidity thereof in yaw and to attenuate ground resonance.
Document FR 2 372 081 describes skid landing gear of the subcritical and rigid type.
In order to damp resonance and impacts on landing on the ground, flexible blades are secured to the rear end of each skid.
Document FR 2 537 542 describes a skid undercarriage for a helicopter with a device for absorbing energy in the event of a crash landing or a hard landing.
In order to limit stresses in a force take-up structure of the aircraft, the energy absorption device is suitable for being subjected to plastic deformation, and it includes at least one damper component, e.g. a hydraulic damper.
With that device, it is desired to avoid the skid support cross-members buckling in compression.
Document FR 2 647 170 seeks to reduce the flexibility of such a damper, e.g. in the context of naval applications, for example.
Document GB 726 573 describes such an aircraft main undercarriage with a pair of frames that are symmetrical about the longitudinal midplane of the aircraft, and with friction skids or beams.
The frames of the landing gear are associated with means for damping irregularities in the landing surface and for damping twisting forces about their hinge axes.
Document U.S. Pat. No. 2,641,423 describes a skid undercarriage for a helicopter that is suitable for providing anticrash functions by irreversible plastic deformation, but without buckling of horizontal cross-members made of aluminum.
Document U.S. Pat. No. 3,716,208 describes a skid landing gear for a helicopter.
That landing gear includes a damper, and a tubular member suitable for absorbing certain forces in the event of a crash landing by measured plastic deformation.
Document U.S. Pat. No. 4,519,559 describes an actuator device arranged to reestablish the stability of a helicopter resting on its skid landing gear.
Each of the skids has two pairs of cross-member elements, with each element being hinged to the take-up structure about a longitudinal axis.
The actuators are interposed between the force take-up structure of the helicopter and the cross-member side elements.
A connection between these elements and each actuator is disposed between the axis of rotation of the element and its respective skid.
In the light of the above, it will be understood firstly that rigid skid undercarriages are often too heavy, too bulky, and too expensive for certain rotary wing aircraft, such as light helicopters.
In contrast to such rigid skid undercarriages, the term “flexible skid undercarriage” is used herein to designate an undercarriage in which energy absorption during a normal landing, a hard landing, or a crash landing is performed solely by transverse elements, skids, and other connection systems deforming in a manner that is elastic or plastic, and without involving any adjoining dampers, side braces, or the like.
Secondly, it will thus be understood that at present no flexible skid undercarriage (i.e. not including a damper) is available that is entirely acceptable in practice, whether from the ground resonance point of view or from the point of view of its specific anticrash behavior.
Complying with one of those criteria conflicts with complying with the other, since such an undercarriage must be capable of deforming flexibly so as to avoid being excessively sensitive to ground resonance, and must also present sufficient strength to absorb the energy involved in a crash landing or a hard landing.